WASHINGTON (AP) — Just a third of Americans back President Barack Obama’s health care overhaul on which the Supreme Court is about to pass judgment, a new poll finds. But there is overwhelming support among both supporters and opponents for Congress and the president to begin work on a new bill if the high court strikes down the two-year-old law.

The overall level of support for the law is relatively unchanged in recent months, with 47 percent opposing it. But an Associated Press-GfK poll shows that only 21 percent of independents approve of the law, a new low in AP-GfK polling.

The Supreme Court is expected to rule on the 2010 law in the next week or so. Most of the law’s major changes aimed at extending health insurance to more than 30 million Americans who now lack coverage have yet to take effect, including the requirement that most people have health insurance or pay a penalty. The insurance mandate has been among the least popular aspects of the law. Provisions that have gone into effect include extended coverage for young adults on their parents’ insurance and relief for seniors with high prescription drug costs.

But whatever people think of the law, they don’t want a Supreme Court ruling against it to be the last word on health care reform. More than three-fourths of Americans want their political leaders to undertake a new effort, rather than leave the health care system alone if the court rules against the law, according to the poll.

Large majorities of both opponents and backers of the law share the view that Congress and the president should start anew. The lowest level of support for new health care legislation comes from people who identify themselves as strong supporters of the tea party. Even in that group, though, nearly 60 percent favor work on a new bill.

Gary Hess, a Republican from Discovery Bay, Calif., wants the high court to throw out the entire law.

But Hess, 77, said he favors the provision requiring insurance companies to cover people regardless of their medical condition. “There needs to be compromise on both sides,” the retired school administrator said.

Garrett Chase, 51, said he hopes the court leaves the law in place but agreed with Hess that the politicians should get back to work if it is struck down. “I live in the ghetto, and I see people dying every day,” said Chase, an unemployed car salesman from Baltimore. “They can’t get help because they can’t afford it.”

A new health care bill doesn’t seem to be in either party’s plans. Republicans say they will try to repeal whatever’s left of the law after the high court rules and then wait at least until after the November elections to push replacement measures. Democrats say Obama will push to put in place whatever survives.

A narrow majority say the outcome of this year’s presidential contest between Obama and his presumed challenger, Republican Mitt Romney, will have a big effect on the nation’s health care system. Republicans, at 58 percent, are most likely to see a link between the election and health care. Forty-eight percent of Democrats and 42 percent of independents believe the election will have a great deal of impact on the health care system.

Obama’s approval rating on handling health care was unchanged compared with polls in May and February. Forty-eight percent approve and 50 percent disapprove of his handling of the issue. Independents’ disapproval of Obama on health care topped 50 percent for the first time since October.

The Associated Press-GfK Poll was conducted June 14-18 by GfK Roper Public Affairs and Corporate Communications. It involved landline and cellphone interviews with 1,007 adults nationwide and has a margin of sampling error of plus or minus 4 percentage points.